I throw Simple Solution into my washer. I don't have pups but I use it whenever I wash the dog bedding and towels and the like. I put maybe 1/4 cup into the detergent container with the detergent and about the same into the softener container of the tray.
I use bleach too, but I also use liquid fabric softener. I'm addicted to the smell of either Downy or Gain Apple Mango Tango. My fleece holds up just fine - I've used bleach for years, plus it kills germs.